74: Potential functions

1

• 7-4 Potential functions
• Vector potential
• was introduced because
• Thus the Faradays law becomes
• i.e.,
• Or

(7.55)
(7.56)
2

• This is allowed because
• Hence
• We wish to work with the two potentials V and
  , which
• have 4 unknowns, then
• Otherwise, one needs to solve with
  6 unknowns.
• We begin with

(7.57)
3

• Using
• i.e.,

(7-60)
4

• Applying the vector identity
• we obtain
• Let
• Lorentz gauge, the one has
• Non-homogeneous wave equation for , where
• velocity appear

5

• To obtain the wave equation for the scalar
  potential V, we
• begin with
• Or
• Hence

(7-65)
6

• 7-5 Electromagnetic Boundary Conditions
• E1tE2t, always.
• B1nB2n, always.
• For PEC, the conductor side H20, E20.

(7.66a)
(7.66b)
(7.66c)
(7.66d)
(7.68)